List of practice Questions

Find the number of $4$ letter words, with or without meaning, which can be formed out of the letters of the word , where the repetition of the letters is not allowed.

Find the mean of first $10$ multiples of $3$.

Find the median of $18, 35, 10, 42, 21 $

Find the magnifying power of a compound microscope whose objective has a focal power of 100 D and eyepiece has a focal power of 16 D when the object is placed at a distance of 1.1 cm from the objective. Assume that the final image is formed at the least distance of distinct vision, 25 cm.

Find the maximum and minimum values of $6sinx\, cosx + 4cos2x$.

Find the maximum profit that a company can make, if the profit function is given by $P(x) = 41 + 24x - 18x^2$.

Find the maximum value of $f(x) = sin(sinx)$ for all $x \in R$

Find the length of latus rectum of the parabola $y^{2} = 8x$.

Find the length of perpendicular from origin to the plane $\vec{r}\cdot\left(3\hat{i}-4\hat{j}-12\hat{k}\right)+39=0$

Find the general solution for the equation $cos4x = cos2x$.

Find the identity element in the set $I^+$ of all positive integers defined by $a * b = a + b$ for all $a$, $b \in I^+$.

Find the inverse of each of the following matrices by using elementary row transformations. $\begin{bmatrix}3&3\\ 2&5\end{bmatrix}$

Find the derivative of $(x^2 + 1)\, cos\, x$.

Find the derivative of $\frac{x^{5}-cos\,x}{sin\,x}$.

Find the distance between the points $P(1, -3, 4)$ and $Q (-4,1,2)$.

Find the equation of line parallel to $y$-axis and drawn through the point of intersection of the line $x - 7y + 5 = 0$ and $3x + y = 0$.

Find the degree measure of the angle subtended at the centre of a circle of radius $100 \,cm$ by an arc of length $22 \,cm$ as shown in figure. [Use $\pi=\frac{22}{7}$]

Find the derivative of $\frac{cos\,x}{1+sin\,x}$.

Find the $C.V.$ of the following data :

Find the circular measure of the following angle $75^{\circ}$

Find the coordinates of the points which trisect the line segment $AB$ where $A(2,1, -3)$ and $B(5, -8,3)$.

Find the angle in radian through which a pendulum swings and its length is $75\, cm$ and tip describes an arc of length $21 \,cm$.

Find the area bounded by the curve $x = 2 - y - y^2$ and y-axis.

Find the area of the largest isosceles triangle having perimeter $18$ metres.

Find perpendicular distance of the line joining the points $(cos \,\theta, sin \,\theta)$ and $(cos\, \phi, sin \,\phi)$ from the origin.